Lesson 1 of 5 · 14 min

Convexity: measuring the curve

Duration draws a straight line through a curved price-yield relationship; convexity measures how much the curve bends away from that line.

In short

Modified duration captures the first-order (linear) effect of a yield change on price. Convexity captures the second-order (non-linear) effect.
For an option-free fixed-rate bond the price-yield curve is convex: the true price always lies above the duration line.
Small yield changes: duration alone is fine. Large yield changes: you need convexity too.
Approximate convexity uses the same three prices as approximate modified duration: $\text{ApproxCon} = \dfrac{PV_- + PV_+ - 2PV_0}{(\Delta y)^2 \, PV_0}$ .
The exact cash-flow method sums $t(t+1) \times w_t$ divided by $(1+r)^2$ , then divides by periods per year squared to annualize.

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